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Register a new userFitting the radial acceleration relation to individual SPARC galaxies
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Pengfei Li
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Galaxies follow a tight radial acceleration relation (RAR): the acceleration observed at every radius correlates with that expected from the distribution of baryons. We use the Markov Chain Monte Carlo method to fit the mean RAR to 175 individual galaxies in the SPARC database, marginalizing over stellar mass-to-light ratio ($Upsilon_{star}$), galaxy distance, and disk inclination. Acceptable fits with astrophysically reasonable parameters are found for the vast majority of galaxies. The residuals around these fits have an rms scatter of only 0.057 dex ($sim$13$%$). This is in agreement with the predictions of modified Newtonian dynamics (MOND). We further consider a generalized version of the RAR that, unlike MOND, permits galaxy-to-galaxy variation in the critical acceleration scale. The fits are not improved with this additional freedom: there is no credible indication of variation in the critical acceleration scale. The data are consistent with the action of a single effective force law. The apparent universality of the acceleration scale and the small residual scatter are key to understanding galaxies.
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The equation of motion in the generally covariant modified gravity (MOG) theory leads, for weak gravitational fields and non-relativistic motion, to a modification of Newtons gravitational acceleration law. In addition to the metric $g_{mu u}$, MOG has a vector field $phi_mu$ that couples with gravitational strength to all baryonic matter. The gravitational coupling strength is determined by the MOG parameter $alpha$, while parameter $mu$ is the small effective mass of $phi_mu$. The MOG acceleration law has been demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet Cluster and Train Wreck Cluster mergers. For the SPARC sample of rotationally supported spiral and irregular galaxies, McGaugh et al. [24] (MLS) have found a radial acceleration relation (RAR) that relates accelerations derived from galaxy rotation curves to Newtonian accelerations derived from galaxy mass models. Using the same SPARC galaxy data, mass models independently derived from that data, and MOG parameters $alpha$ and $mu$ that run with galaxy mass, we demonstrate that adjusting galaxy parameters within $pm 1$-sigma bounds can yield MOG predictions consistent with the given rotational velocity data. Moreover, the same adjusted parameters yield a good fit to the RAR of MLS, with the RAR parameter $a_0=(5.4pm .3)times 10^{-11},{rm m/s^2}$.
Verlinde (2016) has recently proposed that spacetime and gravity may emerge from an underlying microscopic theory. In a de Sitter spacetime, such emergent gravity (EG) contains an additional gravitational force due to dark energy, which may explain the mass discrepancies observed in galactic systems without the need of dark matter. For a point mass, EG is equivalent to Modified Newtonian Dynamics (MOND). We show that this equivalence does not hold for finite-size galaxies: there are significant differences between EG and MOND in the inner regions of galaxies. We confront theoretical predictions with the empirical Radial Acceleration Relation (RAR). We find that (i) EG is consistent with the observed RAR only if we substantially decrease the fiducial stellar mass-to-light ratios; the resulting values are in tension with other astronomical estimates; (ii) EG predicts that the residuals around the RAR should correlate with radius; such residual correlation is not observed.
We study the radial acceleration relation (RAR) between the total ($a_{rm tot}$) and baryonic ($a_{rm bary}$) centripetal acceleration profiles of central galaxies in the cold dark matter (CDM) paradigm. We analytically show that the RAR is intimately connected with the physics of the quasi-adiabatic relaxation of dark matter in the presence of baryons in deep potential wells. This cleanly demonstrates how the mean RAR and its scatter emerge in the low-acceleration regime ($10^{-12},{rm m,s}^{-2}lesssim a_{rm bary}lesssim10^{-10},{rm m,s}^{-2}$) from an interplay between baryonic feedback processes and the distribution of CDM in dark halos. Our framework allows us to go further and study both higher and lower accelerations in detail, using analytical approximations and a realistic mock catalog of $sim342,000$ low-redshift central galaxies with $M_rleq-19$. We show that, while the RAR in the baryon-dominated, high-acceleration regime ($a_{rm bary}gtrsim10^{-10},{rm m,s}^{-2}$) is very sensitive to details of the relaxation physics, a simple `baryonification prescription matching the relaxation results of hydrodynamical CDM simulations is remarkably successful in reproducing the observed RAR without any tuning. And in the (currently unobserved) ultra-low-acceleration regime ($a_{rm bary}lesssim 10^{-12},{rm m,s}^{-2}$), the RAR is sensitive to the abundance of diffuse gas in the halo outskirts, with our default model predicting a distinctive break from a simple power-law-like relation for HI-deficient, diffuse gas-rich centrals. Our mocks also show that the RAR provides more robust, testable predictions of the $Lambda$CDM paradigm at galactic scales, with implications for alternative gravity theories, than the baryonic Tully-Fisher relation.
We study the link between baryons and dark matter in 240 galaxies with spatially resolved kinematic data. Our sample spans 9 dex in stellar mass and includes all morphological types. We consider (i) 153 late-type galaxies (LTGs; spirals and irregulars) with gas rotation curves from the SPARC database; (ii) 25 early-type galaxies (ETGs; ellipticals and lenticulars) with stellar and HI data from ATLAS^3D or X-ray data from Chandra; and (iii) 62 dwarf spheroidals (dSphs) with individual-star spectroscopy. We find that LTGs, ETGs, and classical dSphs follow the same radial acceleration relation: the observed acceleration (gobs) correlates with that expected from the distribution of baryons (gbar) over 4 dex. The relation coincides with the 1:1 line (no dark matter) at high accelerations but systematically deviates from unity below a critical scale of ~10^-10 m/s^2. The observed scatter is remarkably small (<0.13 dex) and largely driven by observational uncertainties. The residuals do not correlate with any global or local galaxy property (baryonic mass, gas fraction, radius, etc.). The radial acceleration relation is tantamount to a Natural Law: when the baryonic contribution is measured, the rotation curve follows, and vice versa. Including ultrafaint dSphs, the relation may extend by another 2 dex and possibly flatten at gbar<10^-12 m/s^2, but these data are significantly more uncertain. The radial acceleration relation subsumes and generalizes several well-known dynamical properties of galaxies, like the Tully-Fisher and Faber-Jackson relations, the baryon-halo conspiracies, and Renzos rule.
A strong correlation has been measured between the observed centripetal accelerations in galaxies and the accelerations implied by the baryonic components of galaxies. This empirical radial acceleration relation must be accounted for in any viable model of galaxy formation. We measure and compare the radial accelerations contributed by baryons and by dark matter in disk galaxies in the MassiveBlack-II hydrodynamic galaxy formation simulation. The sample of 1594 galaxies spans three orders of magnitude in luminosity and four in surface brightness, comparable to the observed sample from the Spitzer Photometry & Accurate Rotation Curves (SPARC) dataset used by McGaugh et al. (2016). We find that radial accelerations contributed by baryonic matter only and by total matter are highly correlated, with only small scatter around their mean or median relation, despite the wide ranges of galaxy luminosity and surface brightness. We further find that the radial acceleration relation in this simulation differs from that of the SPARC sample, and can be described by a simple power law in the acceleration range we are probing.
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